First-Order-Logic
Question 1 |
(a) Show that the product of the least common multiple and the greatest common divisor of two positive integers a and b is a*b.
(b) Consider the following first order formula:
(Ax)(Ey)R(x,y)∧(Ax)(Ay)(R(x,y) → ~R(y,x))
∧(Ax)(Ay)(Az)(R(x,y)∧R(y,z) → R(x,z))
∧(Ax) ~R(x,x)
(A-universal quantifier and E-existential quantifier) Does it have finite models?
Is it satisfiable? Is so, give a countable model for it.
Theory Explanation. |
There is 1 question to complete.